Date of Award

7-2026

Document Type

Dissertation

Degree Name

Doctor of Philosophy (PhD)

Department

Mathematics and Systems Engineering

First Advisor

Munevver Mine Subasi

Second Advisor

Luis Daniel Otero

Third Advisor

Xianqi Li

Fourth Advisor

Son Luu Nguyen

Abstract

Portfolio optimization is a fundamental problem at the intersection of finance, eco nomics, operations research, and applied mathematics. It aims to allocate capital among financial assets in a way that balances return generation and risk control. Classical portfolio optimization approaches, particularly Markowitz’s mean variance framework and related risk-adjusted performance measures, have provided important foundations for portfolio selection. However, these approaches may not fully capture the multiple dimensions of risk faced by risk-averse investors, including downside losses, the frequency of loss occurrences, and the magnitude of extreme losses. These limitations motivate the development of more flexible optimization models that incorporate multiple risk measures, investor preferences, and practical portfolio constraints. This dissertation develops and analyzes six mixed-integer linear programming models for stock portfolio optimization under multiple risk and return objectives, where downside risk, potential loss occurrence, and largest loss magnitude are minimized and expected portfolio return is maximized through a multiple-risk tradeoff framework and through investor-defined objective weights. The utilization and performance of these models are evaluated through computational experiments using real-world stock market data from two distinct financial markets: the Dow Jones Industrial Average (DJIA), representing a mature and developed market, and the Saudi Tadawul market, representing an emerging market. The comparative analysis evaluates each portfolio using down side risk, probability of loss, largest loss magnitude, and portfolio return, allowing the proposed models to be examined across different market structures, risk-return environments, and investor preferences. In addition to the historical average-based optimization framework, this dissertation develops a hybrid forecasting and optimization methodology for portfolio selection. Instead of relying solely on historical average returns, several forecasting methods, including Weighted Moving Average, Linear Regression, Multilayer Perceptron, Gaussian Processes, and Support Vector Machines, are used to forecast future stock returns. These forecasted returns are incorporated into the proposed optimization models and compared with the traditional historical average-based approach through a rolling out-of-sample simulation. This framework provides a practical assessment of how forecast-based return estimates affect portfolio allocation decisions and realized portfolio performance. The computational results demonstrate that the proposed models generate distinct risk-return profiles and provide flexible, investor-oriented portfolio structures that accommodate different risk preferences and return objectives.

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